# Lebesgue measure

In measure theory, a branch of mathematics, the **Lebesgue measure**, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of *n*-dimensional Euclidean space. For *n* = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called ** n-dimensional volume**,

**, or simply**

*n*-volume**volume**.[1] It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called

**Lebesgue-measurable**; the measure of the Lebesgue-measurable set

*A*is here denoted by

*λ*(

*A*).

Henri Lebesgue described this measure in the year 1901, followed the next year by his description of the Lebesgue integral. Both were published as part of his dissertation in 1902.[2]

The Lebesgue measure is often denoted by *dx*, but this should not be confused with the distinct notion of a volume form.